LMFDB - Embedded newform 816.2.bd.a.625.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [816,2,Mod(625,816)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(816, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("816.625");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 816 = 2^{4} \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	816.bd (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.51579280494$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 102)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			625.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	816.625
Dual form			816.2.bd.a.769.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{3} +(0.414214 + 0.414214i) q^{5} +(-3.41421 + 3.41421i) q^{7} +1.00000i q^{9} +(2.82843 - 2.82843i) q^{11} -2.82843 q^{13} -0.585786i q^{15} +(-3.00000 - 2.82843i) q^{17} -6.82843i q^{19} +4.82843 q^{21} +(2.24264 - 2.24264i) q^{23} -4.65685i q^{25} +(0.707107 - 0.707107i) q^{27} +(-0.414214 - 0.414214i) q^{29} +(-0.585786 - 0.585786i) q^{31} -4.00000 q^{33} -2.82843 q^{35} +(-1.58579 - 1.58579i) q^{37} +(2.00000 + 2.00000i) q^{39} +(-2.17157 + 2.17157i) q^{41} -1.65685i q^{43} +(-0.414214 + 0.414214i) q^{45} -12.4853 q^{47} -16.3137i q^{49} +(0.121320 + 4.12132i) q^{51} -2.82843i q^{53} +2.34315 q^{55} +(-4.82843 + 4.82843i) q^{57} +12.4853i q^{59} +(0.757359 - 0.757359i) q^{61} +(-3.41421 - 3.41421i) q^{63} +(-1.17157 - 1.17157i) q^{65} -1.17157 q^{67} -3.17157 q^{69} +(-4.58579 - 4.58579i) q^{71} +(6.65685 + 6.65685i) q^{73} +(-3.29289 + 3.29289i) q^{75} +19.3137i q^{77} +(10.2426 - 10.2426i) q^{79} -1.00000 q^{81} +4.48528i q^{83} +(-0.0710678 - 2.41421i) q^{85} +0.585786i q^{87} +(9.65685 - 9.65685i) q^{91} +0.828427i q^{93} +(2.82843 - 2.82843i) q^{95} +(-9.48528 - 9.48528i) q^{97} +(2.82843 + 2.82843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5} - 8 q^{7} - 12 q^{17} + 8 q^{21} - 8 q^{23} + 4 q^{29} - 8 q^{31} - 16 q^{33} - 12 q^{37} + 8 q^{39} - 20 q^{41} + 4 q^{45} - 16 q^{47} - 8 q^{51} + 32 q^{55} - 8 q^{57} + 20 q^{61} - 8 q^{63}+ \cdots - 4 q^{97}+O(q^{100}) $ 4 * q - 4 * q^5 - 8 * q^7 - 12 * q^17 + 8 * q^21 - 8 * q^23 + 4 * q^29 - 8 * q^31 - 16 * q^33 - 12 * q^37 + 8 * q^39 - 20 * q^41 + 4 * q^45 - 16 * q^47 - 8 * q^51 + 32 * q^55 - 8 * q^57 + 20 * q^61 - 8 * q^63 - 16 * q^65 - 16 * q^67 - 24 * q^69 - 24 * q^71 + 4 * q^73 - 16 * q^75 + 24 * q^79 - 4 * q^81 + 28 * q^85 + 16 * q^91 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/816\mathbb{Z}\right)^\times$.

$n$	$241$	$511$	$545$	$613$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	0.414214	+	0.414214i	0.185242	+	0.185242i	0.793635	−	0.608394i	$-0.208186\pi$
$5$	0.414214	+	0.414214i	0.185242	+	0.185242i	−0.608394	+	0.793635i	$0.708186\pi$
$6$		0			0
$7$	−3.41421	+	3.41421i	−1.29045	+	1.29045i	−0.355944	+	0.934507i	$0.615841\pi$
$7$	−3.41421	+	3.41421i	−1.29045	+	1.29045i	−0.934507	+	0.355944i	$0.884159\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	2.82843	−	2.82843i	0.852803	−	0.852803i	−0.137675	−	0.990478i	$-0.543963\pi$
$11$	2.82843	−	2.82843i	0.852803	−	0.852803i	0.990478	+	0.137675i	$0.0439628\pi$
$12$		0			0
$13$	−2.82843			−0.784465			−0.392232	−	0.919866i	$-0.628297\pi$
$13$	−2.82843			−0.784465			−0.392232	+	0.919866i	$0.628297\pi$
$14$		0			0
$15$		−	0.585786i		−	0.151249i
$16$		0			0
$17$	−3.00000	−	2.82843i	−0.727607	−	0.685994i
$17$	−3.00000	−	2.82843i	−0.727607	−	0.685994i
$18$		0			0
$19$		−	6.82843i		−	1.56655i	−0.621676	−	0.783274i	$-0.713548\pi$
$19$		−	6.82843i		−	1.56655i	0.621676	−	0.783274i	$-0.286452\pi$
$20$		0			0
$21$	4.82843			1.05365
$22$		0			0
$23$	2.24264	−	2.24264i	0.467623	−	0.467623i	−0.433521	−	0.901144i	$-0.642729\pi$
$23$	2.24264	−	2.24264i	0.467623	−	0.467623i	0.901144	+	0.433521i	$0.142729\pi$
$24$		0			0
$25$		−	4.65685i		−	0.931371i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$	−0.414214	−	0.414214i	−0.0769175	−	0.0769175i	0.667601	−	0.744519i	$-0.267321\pi$
$29$	−0.414214	−	0.414214i	−0.0769175	−	0.0769175i	−0.744519	+	0.667601i	$0.767321\pi$
$30$		0			0
$31$	−0.585786	−	0.585786i	−0.105210	−	0.105210i	0.652542	−	0.757752i	$-0.273703\pi$
$31$	−0.585786	−	0.585786i	−0.105210	−	0.105210i	−0.757752	+	0.652542i	$0.773703\pi$
$32$		0			0
$33$	−4.00000			−0.696311
$34$		0			0
$35$	−2.82843			−0.478091
$36$		0			0
$37$	−1.58579	−	1.58579i	−0.260702	−	0.260702i	0.564637	−	0.825339i	$-0.309016\pi$
$37$	−1.58579	−	1.58579i	−0.260702	−	0.260702i	−0.825339	+	0.564637i	$0.809016\pi$
$38$		0			0
$39$	2.00000	+	2.00000i	0.320256	+	0.320256i
$40$		0			0
$41$	−2.17157	+	2.17157i	−0.339143	+	0.339143i	−0.856045	−	0.516902i	$-0.827085\pi$
$41$	−2.17157	+	2.17157i	−0.339143	+	0.339143i	0.516902	+	0.856045i	$0.327085\pi$
$42$		0			0
$43$		−	1.65685i		−	0.252668i	−0.991988	−	0.126334i	$-0.959679\pi$
$43$		−	1.65685i		−	0.252668i	0.991988	−	0.126334i	$-0.0403211\pi$
$44$		0			0
$45$	−0.414214	+	0.414214i	−0.0617473	+	0.0617473i
$46$		0			0
$47$	−12.4853			−1.82117			−0.910583	−	0.413327i	$-0.864367\pi$
$47$	−12.4853			−1.82117			−0.910583	+	0.413327i	$0.864367\pi$
$48$		0			0
$49$		−	16.3137i		−	2.33053i
$50$		0			0
$51$	0.121320	+	4.12132i	0.0169882	+	0.577100i
$52$		0			0
$53$		−	2.82843i		−	0.388514i	−0.980951	−	0.194257i	$-0.937770\pi$
$53$		−	2.82843i		−	0.388514i	0.980951	−	0.194257i	$-0.0622296\pi$
$54$		0			0
$55$	2.34315			0.315950
$56$		0			0
$57$	−4.82843	+	4.82843i	−0.639541	+	0.639541i
$58$		0			0
$59$			12.4853i			1.62545i	0.582651	+	0.812723i	$0.302016\pi$
$59$			12.4853i			1.62545i	−0.582651	+	0.812723i	$0.697984\pi$
$60$		0			0
$61$	0.757359	−	0.757359i	0.0969699	−	0.0969699i	−0.656958	−	0.753928i	$-0.728157\pi$
$61$	0.757359	−	0.757359i	0.0969699	−	0.0969699i	0.753928	+	0.656958i	$0.228157\pi$
$62$		0			0
$63$	−3.41421	−	3.41421i	−0.430150	−	0.430150i
$64$		0			0
$65$	−1.17157	−	1.17157i	−0.145316	−	0.145316i
$66$		0			0
$67$	−1.17157			−0.143130			−0.0715652	−	0.997436i	$-0.522799\pi$
$67$	−1.17157			−0.143130			−0.0715652	+	0.997436i	$0.522799\pi$
$68$		0			0
$69$	−3.17157			−0.381813
$70$		0			0
$71$	−4.58579	−	4.58579i	−0.544233	−	0.544233i	0.380534	−	0.924767i	$-0.375740\pi$
$71$	−4.58579	−	4.58579i	−0.544233	−	0.544233i	−0.924767	+	0.380534i	$0.875740\pi$
$72$		0			0
$73$	6.65685	+	6.65685i	0.779126	+	0.779126i	0.979682	−	0.200556i	$-0.0642750\pi$
$73$	6.65685	+	6.65685i	0.779126	+	0.779126i	−0.200556	+	0.979682i	$0.564275\pi$
$74$		0			0
$75$	−3.29289	+	3.29289i	−0.380231	+	0.380231i
$76$		0			0
$77$			19.3137i			2.20100i
$78$		0			0
$79$	10.2426	−	10.2426i	1.15239	−	1.15239i	0.166314	−	0.986073i	$-0.446813\pi$
$79$	10.2426	−	10.2426i	1.15239	−	1.15239i	0.986073	−	0.166314i	$-0.0531866\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$			4.48528i			0.492324i	0.969229	+	0.246162i	$0.0791695\pi$
$83$			4.48528i			0.492324i	−0.969229	+	0.246162i	$0.920831\pi$
$84$		0			0
$85$	−0.0710678	−	2.41421i	−0.00770839	−	0.261858i
$86$		0			0
$87$			0.585786i			0.0628029i
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$	9.65685	−	9.65685i	1.01231	−	1.01231i
$92$		0			0
$93$			0.828427i			0.0859039i
$94$		0			0
$95$	2.82843	−	2.82843i	0.290191	−	0.290191i
$96$		0			0
$97$	−9.48528	−	9.48528i	−0.963084	−	0.963084i	0.0362581	−	0.999342i	$-0.488456\pi$
$97$	−9.48528	−	9.48528i	−0.963084	−	0.963084i	−0.999342	+	0.0362581i	$0.988456\pi$
$98$		0			0
$99$	2.82843	+	2.82843i	0.284268	+	0.284268i
$100$		0			0
$101$	5.17157			0.514591			0.257295	−	0.966333i	$-0.417169\pi$
$101$	5.17157			0.514591			0.257295	+	0.966333i	$0.417169\pi$
$102$		0			0
$103$	−14.8284			−1.46109			−0.730544	−	0.682865i	$-0.760734\pi$
$103$	−14.8284			−1.46109			−0.730544	+	0.682865i	$0.760734\pi$
$104$		0			0
$105$	2.00000	+	2.00000i	0.195180	+	0.195180i
$106$		0			0
$107$	−9.65685	−	9.65685i	−0.933563	−	0.933563i	0.0643632	−	0.997927i	$-0.479498\pi$
$107$	−9.65685	−	9.65685i	−0.933563	−	0.933563i	−0.997927	+	0.0643632i	$0.979498\pi$
$108$		0			0
$109$	−2.75736	+	2.75736i	−0.264107	+	0.264107i	−0.826720	−	0.562613i	$-0.809796\pi$
$109$	−2.75736	+	2.75736i	−0.264107	+	0.264107i	0.562613	+	0.826720i	$0.309796\pi$
$110$		0			0
$111$			2.24264i			0.212862i
$112$		0			0
$113$	9.00000	−	9.00000i	0.846649	−	0.846649i	−0.143065	−	0.989713i	$-0.545696\pi$
$113$	9.00000	−	9.00000i	0.846649	−	0.846649i	0.989713	+	0.143065i	$0.0456957\pi$
$114$		0			0
$115$	1.85786			0.173247
$116$		0			0
$117$		−	2.82843i		−	0.261488i
$118$		0			0
$119$	19.8995	−	0.585786i	1.82418	−	0.0536990i
$120$		0			0
$121$		−	5.00000i		−	0.454545i
$122$		0			0
$123$	3.07107			0.276909
$124$		0			0
$125$	4.00000	−	4.00000i	0.357771	−	0.357771i
$126$		0			0
$127$		−	13.6569i		−	1.21185i	−0.795522	−	0.605925i	$-0.792803\pi$
$127$		−	13.6569i		−	1.21185i	0.795522	−	0.605925i	$-0.207197\pi$
$128$		0			0
$129$	−1.17157	+	1.17157i	−0.103151	+	0.103151i
$130$		0			0
$131$	13.6569	+	13.6569i	1.19320	+	1.19320i	0.976162	+	0.217043i	$0.0696411\pi$
$131$	13.6569	+	13.6569i	1.19320	+	1.19320i	0.217043	+	0.976162i	$0.430359\pi$
$132$		0			0
$133$	23.3137	+	23.3137i	2.02155	+	2.02155i
$134$		0			0
$135$	0.585786			0.0504165
$136$		0			0
$137$	−17.6569			−1.50853			−0.754263	−	0.656572i	$-0.772006\pi$
$137$	−17.6569			−1.50853			−0.754263	+	0.656572i	$0.772006\pi$
$138$		0			0
$139$	−4.48528	−	4.48528i	−0.380437	−	0.380437i	0.490823	−	0.871259i	$-0.336696\pi$
$139$	−4.48528	−	4.48528i	−0.380437	−	0.380437i	−0.871259	+	0.490823i	$0.836696\pi$
$140$		0			0
$141$	8.82843	+	8.82843i	0.743488	+	0.743488i
$142$		0			0
$143$	−8.00000	+	8.00000i	−0.668994	+	0.668994i
$144$		0			0
$145$		−	0.343146i		−	0.0284967i
$146$		0			0
$147$	−11.5355	+	11.5355i	−0.951435	+	0.951435i
$148$		0			0
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$		0			0
$151$			13.6569i			1.11138i	0.831390	+	0.555690i	$0.187546\pi$
$151$			13.6569i			1.11138i	−0.831390	+	0.555690i	$0.812454\pi$
$152$		0			0
$153$	2.82843	−	3.00000i	0.228665	−	0.242536i
$154$		0			0
$155$		−	0.485281i		−	0.0389787i
$156$		0			0
$157$	6.00000			0.478852			0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000			0.478852			0.239426	+	0.970915i	$0.423041\pi$
$158$		0			0
$159$	−2.00000	+	2.00000i	−0.158610	+	0.158610i
$160$		0			0
$161$			15.3137i			1.20689i
$162$		0			0
$163$	−1.65685	+	1.65685i	−0.129775	+	0.129775i	−0.769011	−	0.639236i	$-0.779251\pi$
$163$	−1.65685	+	1.65685i	−0.129775	+	0.129775i	0.639236	+	0.769011i	$0.279251\pi$
$164$		0			0
$165$	−1.65685	−	1.65685i	−0.128986	−	0.128986i
$166$		0			0
$167$	15.4142	+	15.4142i	1.19279	+	1.19279i	0.976281	+	0.216506i	$0.0694662\pi$
$167$	15.4142	+	15.4142i	1.19279	+	1.19279i	0.216506	+	0.976281i	$0.430534\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$		0			0
$171$	6.82843			0.522183
$172$		0			0
$173$	2.89949	+	2.89949i	0.220445	+	0.220445i	0.808686	−	0.588241i	$-0.200179\pi$
$173$	2.89949	+	2.89949i	0.220445	+	0.220445i	−0.588241	+	0.808686i	$0.700179\pi$
$174$		0			0
$175$	15.8995	+	15.8995i	1.20189	+	1.20189i
$176$		0			0
$177$	8.82843	−	8.82843i	0.663585	−	0.663585i
$178$		0			0
$179$			12.9706i			0.969465i	0.874662	+	0.484733i	$0.161083\pi$
$179$			12.9706i			0.969465i	−0.874662	+	0.484733i	$0.838917\pi$
$180$		0			0
$181$	−5.58579	+	5.58579i	−0.415188	+	0.415188i	−0.883541	−	0.468353i	$-0.844848\pi$
$181$	−5.58579	+	5.58579i	−0.415188	+	0.415188i	0.468353	+	0.883541i	$0.344848\pi$
$182$		0			0
$183$	−1.07107			−0.0791756
$184$		0			0
$185$		−	1.31371i		−	0.0965858i
$186$		0			0
$187$	−16.4853	+	0.485281i	−1.20552	+	0.0354873i
$188$		0			0
$189$			4.82843i			0.351216i
$190$		0			0
$191$	−1.17157			−0.0847720			−0.0423860	−	0.999101i	$-0.513496\pi$
$191$	−1.17157			−0.0847720			−0.0423860	+	0.999101i	$0.513496\pi$
$192$		0			0
$193$	−4.17157	+	4.17157i	−0.300276	+	0.300276i	−0.841122	−	0.540846i	$-0.818104\pi$
$193$	−4.17157	+	4.17157i	−0.300276	+	0.300276i	0.540846	+	0.841122i	$0.318104\pi$
$194$		0			0
$195$			1.65685i			0.118650i
$196$		0			0
$197$	−7.24264	+	7.24264i	−0.516017	+	0.516017i	−0.916364	−	0.400347i	$-0.868890\pi$
$197$	−7.24264	+	7.24264i	−0.516017	+	0.516017i	0.400347	+	0.916364i	$0.368890\pi$
$198$		0			0
$199$	0.585786	+	0.585786i	0.0415253	+	0.0415253i	0.727565	−	0.686039i	$-0.240652\pi$
$199$	0.585786	+	0.585786i	0.0415253	+	0.0415253i	−0.686039	+	0.727565i	$0.740652\pi$
$200$		0			0
$201$	0.828427	+	0.828427i	0.0584327	+	0.0584327i
$202$		0			0
$203$	2.82843			0.198517
$204$		0			0
$205$	−1.79899			−0.125647
$206$		0			0
$207$	2.24264	+	2.24264i	0.155874	+	0.155874i
$208$		0			0
$209$	−19.3137	−	19.3137i	−1.33596	−	1.33596i
$210$		0			0
$211$	20.4853	−	20.4853i	1.41026	−	1.41026i	0.652329	−	0.757936i	$-0.273792\pi$
$211$	20.4853	−	20.4853i	1.41026	−	1.41026i	0.757936	−	0.652329i	$-0.226208\pi$
$212$		0			0
$213$			6.48528i			0.444364i
$214$		0			0
$215$	0.686292	−	0.686292i	0.0468047	−	0.0468047i
$216$		0			0
$217$	4.00000			0.271538
$218$		0			0
$219$		−	9.41421i		−	0.636154i
$220$		0			0
$221$	8.48528	+	8.00000i	0.570782	+	0.538138i
$222$		0			0
$223$			6.82843i			0.457265i	0.973513	+	0.228633i	$0.0734255\pi$
$223$			6.82843i			0.457265i	−0.973513	+	0.228633i	$0.926575\pi$
$224$		0			0
$225$	4.65685			0.310457
$226$		0			0
$227$	12.4853	−	12.4853i	0.828677	−	0.828677i	−0.158657	−	0.987334i	$-0.550716\pi$
$227$	12.4853	−	12.4853i	0.828677	−	0.828677i	0.987334	+	0.158657i	$0.0507163\pi$
$228$		0			0
$229$		−	14.0000i		−	0.925146i	−0.886581	−	0.462573i	$-0.846926\pi$
$229$		−	14.0000i		−	0.925146i	0.886581	−	0.462573i	$-0.153074\pi$
$230$		0			0
$231$	13.6569	−	13.6569i	0.898555	−	0.898555i
$232$		0			0
$233$	9.00000	+	9.00000i	0.589610	+	0.589610i	0.937526	−	0.347916i	$-0.113111\pi$
$233$	9.00000	+	9.00000i	0.589610	+	0.589610i	−0.347916	+	0.937526i	$0.613111\pi$
$234$		0			0
$235$	−5.17157	−	5.17157i	−0.337356	−	0.337356i
$236$		0			0
$237$	−14.4853			−0.940920
$238$		0			0
$239$	−12.4853			−0.807606			−0.403803	−	0.914846i	$-0.632312\pi$
$239$	−12.4853			−0.807606			−0.403803	+	0.914846i	$0.632312\pi$
$240$		0			0
$241$	−5.82843	−	5.82843i	−0.375442	−	0.375442i	0.494013	−	0.869455i	$-0.335530\pi$
$241$	−5.82843	−	5.82843i	−0.375442	−	0.375442i	−0.869455	+	0.494013i	$0.835530\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	6.75736	−	6.75736i	0.431712	−	0.431712i
$246$		0			0
$247$			19.3137i			1.22890i
$248$		0			0
$249$	3.17157	−	3.17157i	0.200990	−	0.200990i
$250$		0			0
$251$	−17.6569			−1.11449			−0.557245	−	0.830348i	$-0.688142\pi$
$251$	−17.6569			−1.11449			−0.557245	+	0.830348i	$0.688142\pi$
$252$		0			0
$253$		−	12.6863i		−	0.797580i
$254$		0			0
$255$	−1.65685	+	1.75736i	−0.103756	+	0.110050i
$256$		0			0
$257$			29.3137i			1.82854i	0.405107	+	0.914269i	$0.367234\pi$
$257$			29.3137i			1.82854i	−0.405107	+	0.914269i	$0.632766\pi$
$258$		0			0
$259$	10.8284			0.672846
$260$		0			0
$261$	0.414214	−	0.414214i	0.0256392	−	0.0256392i
$262$		0			0
$263$		−	10.1421i		−	0.625391i	−0.949853	−	0.312695i	$-0.898768\pi$
$263$		−	10.1421i		−	0.625391i	0.949853	−	0.312695i	$-0.101232\pi$
$264$		0			0
$265$	1.17157	−	1.17157i	0.0719691	−	0.0719691i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.58579	−	3.58579i	−0.218629	−	0.218629i	0.589291	−	0.807921i	$-0.299407\pi$
$269$	−3.58579	−	3.58579i	−0.218629	−	0.218629i	−0.807921	+	0.589291i	$0.799407\pi$
$270$		0			0
$271$	−21.6569			−1.31556			−0.657780	−	0.753210i	$-0.728504\pi$
$271$	−21.6569			−1.31556			−0.657780	+	0.753210i	$0.728504\pi$
$272$		0			0
$273$	−13.6569			−0.826550
$274$		0			0
$275$	−13.1716	−	13.1716i	−0.794276	−	0.794276i
$276$		0			0
$277$	−6.89949	−	6.89949i	−0.414550	−	0.414550i	0.468770	−	0.883320i	$-0.344697\pi$
$277$	−6.89949	−	6.89949i	−0.414550	−	0.414550i	−0.883320	+	0.468770i	$0.844697\pi$
$278$		0			0
$279$	0.585786	−	0.585786i	0.0350701	−	0.0350701i
$280$		0			0
$281$		−	19.3137i		−	1.15216i	−0.817394	−	0.576080i	$-0.804582\pi$
$281$		−	19.3137i		−	1.15216i	0.817394	−	0.576080i	$-0.195418\pi$
$282$		0			0
$283$	−5.65685	+	5.65685i	−0.336265	+	0.336265i	−0.854960	−	0.518695i	$-0.826418\pi$
$283$	−5.65685	+	5.65685i	−0.336265	+	0.336265i	0.518695	+	0.854960i	$0.326418\pi$
$284$		0			0
$285$	−4.00000			−0.236940
$286$		0			0
$287$		−	14.8284i		−	0.875294i
$288$		0			0
$289$	1.00000	+	16.9706i	0.0588235	+	0.998268i
$290$		0			0
$291$			13.4142i			0.786355i
$292$		0			0
$293$	9.31371			0.544113			0.272056	−	0.962281i	$-0.412296\pi$
$293$	9.31371			0.544113			0.272056	+	0.962281i	$0.412296\pi$
$294$		0			0
$295$	−5.17157	+	5.17157i	−0.301101	+	0.301101i
$296$		0			0
$297$		−	4.00000i		−	0.232104i
$298$		0			0
$299$	−6.34315	+	6.34315i	−0.366834	+	0.366834i
$300$		0			0
$301$	5.65685	+	5.65685i	0.326056	+	0.326056i
$302$		0			0
$303$	−3.65685	−	3.65685i	−0.210081	−	0.210081i
$304$		0			0
$305$	0.627417			0.0359258
$306$		0			0
$307$	6.34315			0.362022			0.181011	−	0.983481i	$-0.442063\pi$
$307$	6.34315			0.362022			0.181011	+	0.983481i	$0.442063\pi$
$308$		0			0
$309$	10.4853	+	10.4853i	0.596487	+	0.596487i
$310$		0			0
$311$	−0.585786	−	0.585786i	−0.0332169	−	0.0332169i	0.690303	−	0.723520i	$-0.257477\pi$
$311$	−0.585786	−	0.585786i	−0.0332169	−	0.0332169i	−0.723520	+	0.690303i	$0.757477\pi$
$312$		0			0
$313$	7.14214	−	7.14214i	0.403697	−	0.403697i	−0.475836	−	0.879534i	$-0.657855\pi$
$313$	7.14214	−	7.14214i	0.403697	−	0.403697i	0.879534	+	0.475836i	$0.157855\pi$
$314$		0			0
$315$		−	2.82843i		−	0.159364i
$316$		0			0
$317$	−15.2426	+	15.2426i	−0.856112	+	0.856112i	−0.990878	−	0.134766i	$-0.956972\pi$
$317$	−15.2426	+	15.2426i	−0.856112	+	0.856112i	0.134766	+	0.990878i	$0.456972\pi$
$318$		0			0
$319$	−2.34315			−0.131191
$320$		0			0
$321$			13.6569i			0.762251i
$322$		0			0
$323$	−19.3137	+	20.4853i	−1.07464	+	1.13983i
$324$		0			0
$325$			13.1716i			0.730627i
$326$		0			0
$327$	3.89949			0.215643
$328$		0			0
$329$	42.6274	−	42.6274i	2.35013	−	2.35013i
$330$		0			0
$331$		−	18.6274i		−	1.02386i	−0.859029	−	0.511928i	$-0.828932\pi$
$331$		−	18.6274i		−	1.02386i	0.859029	−	0.511928i	$-0.171068\pi$
$332$		0			0
$333$	1.58579	−	1.58579i	0.0869006	−	0.0869006i
$334$		0			0
$335$	−0.485281	−	0.485281i	−0.0265138	−	0.0265138i
$336$		0			0
$337$	9.00000	+	9.00000i	0.490261	+	0.490261i	0.908388	−	0.418127i	$-0.137313\pi$
$337$	9.00000	+	9.00000i	0.490261	+	0.490261i	−0.418127	+	0.908388i	$0.637313\pi$
$338$		0			0
$339$	−12.7279			−0.691286
$340$		0			0
$341$	−3.31371			−0.179447
$342$		0			0
$343$	31.7990	+	31.7990i	1.71698	+	1.71698i
$344$		0			0
$345$	−1.31371	−	1.31371i	−0.0707277	−	0.0707277i
$346$		0			0
$347$	8.00000	−	8.00000i	0.429463	−	0.429463i	−0.458983	−	0.888445i	$-0.651786\pi$
$347$	8.00000	−	8.00000i	0.429463	−	0.429463i	0.888445	+	0.458983i	$0.151786\pi$
$348$		0			0
$349$		−	10.8284i		−	0.579632i	−0.957082	−	0.289816i	$-0.906406\pi$
$349$		−	10.8284i		−	0.579632i	0.957082	−	0.289816i	$-0.0935942\pi$
$350$		0			0
$351$	−2.00000	+	2.00000i	−0.106752	+	0.106752i
$352$		0			0
$353$	−12.6274			−0.672090			−0.336045	−	0.941846i	$-0.609089\pi$
$353$	−12.6274			−0.672090			−0.336045	+	0.941846i	$0.609089\pi$
$354$		0			0
$355$		−	3.79899i		−	0.201629i
$356$		0			0
$357$	−14.4853	−	13.6569i	−0.766642	−	0.722797i
$358$		0			0
$359$		−	16.0000i		−	0.844448i	−0.906492	−	0.422224i	$-0.861250\pi$
$359$		−	16.0000i		−	0.844448i	0.906492	−	0.422224i	$-0.138750\pi$
$360$		0			0
$361$	−27.6274			−1.45407
$362$		0			0
$363$	−3.53553	+	3.53553i	−0.185567	+	0.185567i
$364$		0			0
$365$			5.51472i			0.288654i
$366$		0			0
$367$	12.3848	−	12.3848i	0.646480	−	0.646480i	−0.305661	−	0.952141i	$-0.598877\pi$
$367$	12.3848	−	12.3848i	0.646480	−	0.646480i	0.952141	+	0.305661i	$0.0988773\pi$
$368$		0			0
$369$	−2.17157	−	2.17157i	−0.113048	−	0.113048i
$370$		0			0
$371$	9.65685	+	9.65685i	0.501359	+	0.501359i
$372$		0			0
$373$	19.7990			1.02515			0.512576	−	0.858642i	$-0.328691\pi$
$373$	19.7990			1.02515			0.512576	+	0.858642i	$0.328691\pi$
$374$		0			0
$375$	−5.65685			−0.292119
$376$		0			0
$377$	1.17157	+	1.17157i	0.0603391	+	0.0603391i
$378$		0			0
$379$	−17.6569	−	17.6569i	−0.906972	−	0.906972i	0.0890550	−	0.996027i	$-0.471615\pi$
$379$	−17.6569	−	17.6569i	−0.906972	−	0.906972i	−0.996027	+	0.0890550i	$0.971615\pi$
$380$		0			0
$381$	−9.65685	+	9.65685i	−0.494736	+	0.494736i
$382$		0			0
$383$		−	23.7990i		−	1.21607i	−0.793910	−	0.608036i	$-0.791958\pi$
$383$		−	23.7990i		−	1.21607i	0.793910	−	0.608036i	$-0.208042\pi$
$384$		0			0
$385$	−8.00000	+	8.00000i	−0.407718	+	0.407718i
$386$		0			0
$387$	1.65685			0.0842226
$388$		0			0
$389$			36.6274i			1.85708i	0.371228	+	0.928542i	$0.378937\pi$
$389$			36.6274i			1.85708i	−0.371228	+	0.928542i	$0.621063\pi$
$390$		0			0
$391$	−13.0711	+	0.384776i	−0.661032	+	0.0194590i
$392$		0			0
$393$		−	19.3137i		−	0.974248i
$394$		0			0
$395$	8.48528			0.426941
$396$		0			0
$397$	23.3848	−	23.3848i	1.17365	−	1.17365i	0.192315	−	0.981333i	$-0.438400\pi$
$397$	23.3848	−	23.3848i	1.17365	−	1.17365i	0.981333	−	0.192315i	$-0.0615995\pi$
$398$		0			0
$399$		−	32.9706i		−	1.65059i
$400$		0			0
$401$	−6.17157	+	6.17157i	−0.308194	+	0.308194i	−0.844209	−	0.536015i	$-0.819929\pi$
$401$	−6.17157	+	6.17157i	−0.308194	+	0.308194i	0.536015	+	0.844209i	$0.319929\pi$
$402$		0			0
$403$	1.65685	+	1.65685i	0.0825338	+	0.0825338i
$404$		0			0
$405$	−0.414214	−	0.414214i	−0.0205824	−	0.0205824i
$406$		0			0
$407$	−8.97056			−0.444654
$408$		0			0
$409$	−14.0000			−0.692255			−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000			−0.692255			−0.346128	+	0.938187i	$0.612504\pi$
$410$		0			0
$411$	12.4853	+	12.4853i	0.615854	+	0.615854i
$412$		0			0
$413$	−42.6274	−	42.6274i	−2.09756	−	2.09756i
$414$		0			0
$415$	−1.85786	+	1.85786i	−0.0911990	+	0.0911990i
$416$		0			0
$417$			6.34315i			0.310625i
$418$		0			0
$419$	−1.17157	+	1.17157i	−0.0572351	+	0.0572351i	−0.735145	−	0.677910i	$-0.762886\pi$
$419$	−1.17157	+	1.17157i	−0.0572351	+	0.0572351i	0.677910	+	0.735145i	$0.262886\pi$
$420$		0			0
$421$	−15.5147			−0.756141			−0.378071	−	0.925777i	$-0.623412\pi$
$421$	−15.5147			−0.756141			−0.378071	+	0.925777i	$0.623412\pi$
$422$		0			0
$423$		−	12.4853i		−	0.607055i
$424$		0			0
$425$	−13.1716	+	13.9706i	−0.638915	+	0.677672i
$426$		0			0
$427$			5.17157i			0.250270i
$428$		0			0
$429$	11.3137			0.546231
$430$		0			0
$431$	14.2426	−	14.2426i	0.686044	−	0.686044i	−0.275311	−	0.961355i	$-0.588781\pi$
$431$	14.2426	−	14.2426i	0.686044	−	0.686044i	0.961355	+	0.275311i	$0.0887809\pi$
$432$		0			0
$433$		−	16.6274i		−	0.799063i	−0.916720	−	0.399531i	$-0.869173\pi$
$433$		−	16.6274i		−	0.799063i	0.916720	−	0.399531i	$-0.130827\pi$
$434$		0			0
$435$	−0.242641	+	0.242641i	−0.0116337	+	0.0116337i
$436$		0			0
$437$	−15.3137	−	15.3137i	−0.732554	−	0.732554i
$438$		0			0
$439$	9.55635	+	9.55635i	0.456100	+	0.456100i	0.897373	−	0.441273i	$-0.145473\pi$
$439$	9.55635	+	9.55635i	0.456100	+	0.456100i	−0.441273	+	0.897373i	$0.645473\pi$
$440$		0			0
$441$	16.3137			0.776843
$442$		0			0
$443$	28.9706			1.37643			0.688216	−	0.725505i	$-0.258394\pi$
$443$	28.9706			1.37643			0.688216	+	0.725505i	$0.258394\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−7.07107	−	7.07107i	−0.334450	−	0.334450i
$448$		0			0
$449$	8.51472	−	8.51472i	0.401834	−	0.401834i	−0.477045	−	0.878879i	$-0.658292\pi$
$449$	8.51472	−	8.51472i	0.401834	−	0.401834i	0.878879	+	0.477045i	$0.158292\pi$
$450$		0			0
$451$			12.2843i			0.578444i
$452$		0			0
$453$	9.65685	−	9.65685i	0.453719	−	0.453719i
$454$		0			0
$455$	8.00000			0.375046
$456$		0			0
$457$			2.68629i			0.125659i	0.998024	+	0.0628297i	$0.0200125\pi$
$457$			2.68629i			0.125659i	−0.998024	+	0.0628297i	$0.979988\pi$
$458$		0			0
$459$	−4.12132	+	0.121320i	−0.192367	+	0.00566275i
$460$		0			0
$461$		−	25.4558i		−	1.18560i	−0.805351	−	0.592798i	$-0.798023\pi$
$461$		−	25.4558i		−	1.18560i	0.805351	−	0.592798i	$-0.201977\pi$
$462$		0			0
$463$	−6.82843			−0.317344			−0.158672	−	0.987331i	$-0.550721\pi$
$463$	−6.82843			−0.317344			−0.158672	+	0.987331i	$0.550721\pi$
$464$		0			0
$465$	−0.343146	+	0.343146i	−0.0159130	+	0.0159130i
$466$		0			0
$467$			28.0000i			1.29569i	0.761774	+	0.647843i	$0.224329\pi$
$467$			28.0000i			1.29569i	−0.761774	+	0.647843i	$0.775671\pi$
$468$		0			0
$469$	4.00000	−	4.00000i	0.184703	−	0.184703i
$470$		0			0
$471$	−4.24264	−	4.24264i	−0.195491	−	0.195491i
$472$		0			0
$473$	−4.68629	−	4.68629i	−0.215476	−	0.215476i
$474$		0			0
$475$	−31.7990			−1.45904
$476$		0			0
$477$	2.82843			0.129505
$478$		0			0
$479$	5.07107	+	5.07107i	0.231703	+	0.231703i	0.813403	−	0.581700i	$-0.197612\pi$
$479$	5.07107	+	5.07107i	0.231703	+	0.231703i	−0.581700	+	0.813403i	$0.697612\pi$
$480$		0			0
$481$	4.48528	+	4.48528i	0.204511	+	0.204511i
$482$		0			0
$483$	10.8284	−	10.8284i	0.492710	−	0.492710i
$484$		0			0
$485$		−	7.85786i		−	0.356807i
$486$		0			0
$487$	−29.0711	+	29.0711i	−1.31734	+	1.31734i	−0.401459	+	0.915877i	$0.631497\pi$
$487$	−29.0711	+	29.0711i	−1.31734	+	1.31734i	−0.915877	+	0.401459i	$0.868503\pi$
$488$		0			0
$489$	2.34315			0.105961
$490$		0			0
$491$		−	16.2843i		−	0.734899i	−0.930043	−	0.367449i	$-0.880231\pi$
$491$		−	16.2843i		−	0.734899i	0.930043	−	0.367449i	$-0.119769\pi$
$492$		0			0
$493$	0.0710678	+	2.41421i	0.00320073	+	0.108731i
$494$		0			0
$495$			2.34315i			0.105317i
$496$		0			0
$497$	31.3137			1.40461
$498$		0			0
$499$	17.6569	−	17.6569i	0.790429	−	0.790429i	−0.191135	−	0.981564i	$-0.561217\pi$
$499$	17.6569	−	17.6569i	0.790429	−	0.790429i	0.981564	+	0.191135i	$0.0612167\pi$
$500$		0			0
$501$		−	21.7990i		−	0.973907i
$502$		0			0
$503$	−6.72792	+	6.72792i	−0.299983	+	0.299983i	−0.841007	−	0.541024i	$-0.818037\pi$
$503$	−6.72792	+	6.72792i	−0.299983	+	0.299983i	0.541024	+	0.841007i	$0.318037\pi$
$504$		0			0
$505$	2.14214	+	2.14214i	0.0953238	+	0.0953238i
$506$		0			0
$507$	3.53553	+	3.53553i	0.157019	+	0.157019i
$508$		0			0
$509$	2.68629			0.119068			0.0595339	−	0.998226i	$-0.481039\pi$
$509$	2.68629			0.119068			0.0595339	+	0.998226i	$0.481039\pi$
$510$		0			0
$511$	−45.4558			−2.01085
$512$		0			0
$513$	−4.82843	−	4.82843i	−0.213180	−	0.213180i
$514$		0			0
$515$	−6.14214	−	6.14214i	−0.270655	−	0.270655i
$516$		0			0
$517$	−35.3137	+	35.3137i	−1.55310	+	1.55310i
$518$		0			0
$519$		−	4.10051i		−	0.179992i
$520$		0			0
$521$	−5.48528	+	5.48528i	−0.240315	+	0.240315i	−0.816980	−	0.576666i	$-0.804354\pi$
$521$	−5.48528	+	5.48528i	−0.240315	+	0.240315i	0.576666	+	0.816980i	$0.304354\pi$
$522$		0			0
$523$	18.1421			0.793300			0.396650	−	0.917970i	$-0.370173\pi$
$523$	18.1421			0.793300			0.396650	+	0.917970i	$0.370173\pi$
$524$		0			0
$525$		−	22.4853i		−	0.981338i
$526$		0			0
$527$	0.100505	+	3.41421i	0.00437807	+	0.148725i
$528$		0			0
$529$			12.9411i			0.562658i
$530$		0			0
$531$	−12.4853			−0.541815
$532$		0			0
$533$	6.14214	−	6.14214i	0.266045	−	0.266045i
$534$		0			0
$535$		−	8.00000i		−	0.345870i
$536$		0			0
$537$	9.17157	−	9.17157i	0.395783	−	0.395783i
$538$		0			0
$539$	−46.1421	−	46.1421i	−1.98748	−	1.98748i
$540$		0			0
$541$	−12.8995	−	12.8995i	−0.554593	−	0.554593i	0.373170	−	0.927763i	$-0.378271\pi$
$541$	−12.8995	−	12.8995i	−0.554593	−	0.554593i	−0.927763	+	0.373170i	$0.878271\pi$
$542$		0			0
$543$	7.89949			0.339000
$544$		0			0
$545$	−2.28427			−0.0978474
$546$		0			0
$547$	13.1716	+	13.1716i	0.563176	+	0.563176i	0.930208	−	0.367032i	$-0.119626\pi$
$547$	13.1716	+	13.1716i	0.563176	+	0.563176i	−0.367032	+	0.930208i	$0.619626\pi$
$548$		0			0
$549$	0.757359	+	0.757359i	0.0323233	+	0.0323233i
$550$		0			0
$551$	−2.82843	+	2.82843i	−0.120495	+	0.120495i
$552$		0			0
$553$			69.9411i			2.97420i
$554$		0			0
$555$	−0.928932	+	0.928932i	−0.0394310	+	0.0394310i
$556$		0			0
$557$	8.48528			0.359533			0.179766	−	0.983709i	$-0.442466\pi$
$557$	8.48528			0.359533			0.179766	+	0.983709i	$0.442466\pi$
$558$		0			0
$559$			4.68629i			0.198209i
$560$		0			0
$561$	12.0000	+	11.3137i	0.506640	+	0.477665i
$562$		0			0
$563$		−	3.51472i		−	0.148128i	−0.997254	−	0.0740639i	$-0.976403\pi$
$563$		−	3.51472i		−	0.148128i	0.997254	−	0.0740639i	$-0.0235969\pi$
$564$		0			0
$565$	7.45584			0.313670
$566$		0			0
$567$	3.41421	−	3.41421i	0.143383	−	0.143383i
$568$		0			0
$569$		−	12.9706i		−	0.543754i	−0.962332	−	0.271877i	$-0.912356\pi$
$569$		−	12.9706i		−	0.543754i	0.962332	−	0.271877i	$-0.0876444\pi$
$570$		0			0
$571$	−6.14214	+	6.14214i	−0.257040	+	0.257040i	−0.823849	−	0.566809i	$-0.808178\pi$
$571$	−6.14214	+	6.14214i	−0.257040	+	0.257040i	0.566809	+	0.823849i	$0.308178\pi$
$572$		0			0
$573$	0.828427	+	0.828427i	0.0346080	+	0.0346080i
$574$		0			0
$575$	−10.4437	−	10.4437i	−0.435530	−	0.435530i
$576$		0			0
$577$	−3.31371			−0.137951			−0.0689757	−	0.997618i	$-0.521973\pi$
$577$	−3.31371			−0.137951			−0.0689757	+	0.997618i	$0.521973\pi$
$578$		0			0
$579$	5.89949			0.245175
$580$		0			0
$581$	−15.3137	−	15.3137i	−0.635320	−	0.635320i
$582$		0			0
$583$	−8.00000	−	8.00000i	−0.331326	−	0.331326i
$584$		0			0
$585$	1.17157	−	1.17157i	0.0484386	−	0.0484386i
$586$		0			0
$587$			36.9706i			1.52594i	0.646435	+	0.762969i	$0.276259\pi$
$587$			36.9706i			1.52594i	−0.646435	+	0.762969i	$0.723741\pi$
$588$		0			0
$589$	−4.00000	+	4.00000i	−0.164817	+	0.164817i
$590$		0			0
$591$	10.2426			0.421326
$592$		0			0
$593$		−	4.00000i		−	0.164260i	−0.996622	−	0.0821302i	$-0.973828\pi$
$593$		−	4.00000i		−	0.164260i	0.996622	−	0.0821302i	$-0.0261723\pi$
$594$		0			0
$595$	8.48528	+	8.00000i	0.347863	+	0.327968i
$596$		0			0
$597$		−	0.828427i		−	0.0339053i
$598$		0			0
$599$	30.6274			1.25140			0.625701	−	0.780063i	$-0.284813\pi$
$599$	30.6274			1.25140			0.625701	+	0.780063i	$0.284813\pi$
$600$		0			0
$601$	−4.65685	+	4.65685i	−0.189957	+	0.189957i	−0.795678	−	0.605720i	$-0.792885\pi$
$601$	−4.65685	+	4.65685i	−0.189957	+	0.189957i	0.605720	+	0.795678i	$0.292885\pi$
$602$		0			0
$603$		−	1.17157i		−	0.0477101i
$604$		0			0
$605$	2.07107	−	2.07107i	0.0842009	−	0.0842009i
$606$		0			0
$607$	−7.41421	−	7.41421i	−0.300934	−	0.300934i	0.540445	−	0.841379i	$-0.318256\pi$
$607$	−7.41421	−	7.41421i	−0.300934	−	0.300934i	−0.841379	+	0.540445i	$0.818256\pi$
$608$		0			0
$609$	−2.00000	−	2.00000i	−0.0810441	−	0.0810441i
$610$		0			0
$611$	35.3137			1.42864
$612$		0			0
$613$	−21.3137			−0.860853			−0.430426	−	0.902626i	$-0.641637\pi$
$613$	−21.3137			−0.860853			−0.430426	+	0.902626i	$0.641637\pi$
$614$		0			0
$615$	1.27208	+	1.27208i	0.0512951	+	0.0512951i
$616$		0			0
$617$	10.6569	+	10.6569i	0.429029	+	0.429029i	0.888297	−	0.459269i	$-0.151888\pi$
$617$	10.6569	+	10.6569i	0.429029	+	0.429029i	−0.459269	+	0.888297i	$0.651888\pi$
$618$		0			0
$619$	16.9706	−	16.9706i	0.682105	−	0.682105i	−0.278370	−	0.960474i	$-0.589794\pi$
$619$	16.9706	−	16.9706i	0.682105	−	0.682105i	0.960474	+	0.278370i	$0.0897940\pi$
$620$		0			0
$621$		−	3.17157i		−	0.127271i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−19.9706			−0.798823
$626$		0			0
$627$			27.3137i			1.09080i
$628$		0			0
$629$	0.272078	+	9.24264i	0.0108485	+	0.368528i
$630$		0			0
$631$			26.1421i			1.04070i	0.853952	+	0.520351i	$0.174199\pi$
$631$			26.1421i			1.04070i	−0.853952	+	0.520351i	$0.825801\pi$
$632$		0			0
$633$	−28.9706			−1.15148
$634$		0			0
$635$	5.65685	−	5.65685i	0.224485	−	0.224485i
$636$		0			0
$637$			46.1421i			1.82822i
$638$		0			0
$639$	4.58579	−	4.58579i	0.181411	−	0.181411i
$640$		0			0
$641$	13.4853	+	13.4853i	0.532637	+	0.532637i	0.921356	−	0.388720i	$-0.127082\pi$
$641$	13.4853	+	13.4853i	0.532637	+	0.532637i	−0.388720	+	0.921356i	$0.627082\pi$
$642$		0			0
$643$	−0.485281	−	0.485281i	−0.0191376	−	0.0191376i	0.697473	−	0.716611i	$-0.254308\pi$
$643$	−0.485281	−	0.485281i	−0.0191376	−	0.0191376i	−0.716611	+	0.697473i	$0.754308\pi$
$644$		0			0
$645$	−0.970563			−0.0382159
$646$		0			0
$647$	−38.4264			−1.51070			−0.755349	−	0.655323i	$-0.772533\pi$
$647$	−38.4264			−1.51070			−0.755349	+	0.655323i	$0.772533\pi$
$648$		0			0
$649$	35.3137	+	35.3137i	1.38618	+	1.38618i
$650$		0			0
$651$	−2.82843	−	2.82843i	−0.110855	−	0.110855i
$652$		0			0
$653$	22.2132	−	22.2132i	0.869270	−	0.869270i	−0.123122	−	0.992392i	$-0.539291\pi$
$653$	22.2132	−	22.2132i	0.869270	−	0.869270i	0.992392	+	0.123122i	$0.0392906\pi$
$654$		0			0
$655$			11.3137i			0.442063i
$656$		0			0
$657$	−6.65685	+	6.65685i	−0.259709	+	0.259709i
$658$		0			0
$659$	−3.51472			−0.136914			−0.0684570	−	0.997654i	$-0.521808\pi$
$659$	−3.51472			−0.136914			−0.0684570	+	0.997654i	$0.521808\pi$
$660$		0			0
$661$			30.1421i			1.17239i	0.810169	+	0.586197i	$0.199375\pi$
$661$			30.1421i			1.17239i	−0.810169	+	0.586197i	$0.800625\pi$
$662$		0			0
$663$	−0.343146	−	11.6569i	−0.0133267	−	0.452715i
$664$		0			0
$665$			19.3137i			0.748953i
$666$		0			0
$667$	−1.85786			−0.0719368
$668$		0			0
$669$	4.82843	−	4.82843i	0.186678	−	0.186678i
$670$		0			0
$671$		−	4.28427i		−	0.165392i
$672$		0			0
$673$	25.1421	−	25.1421i	0.969158	−	0.969158i	−0.0303803	−	0.999538i	$-0.509672\pi$
$673$	25.1421	−	25.1421i	0.969158	−	0.969158i	0.999538	+	0.0303803i	$0.00967184\pi$
$674$		0			0
$675$	−3.29289	−	3.29289i	−0.126744	−	0.126744i
$676$		0			0
$677$	20.0711	+	20.0711i	0.771394	+	0.771394i	0.978350	−	0.206956i	$-0.0663558\pi$
$677$	20.0711	+	20.0711i	0.771394	+	0.771394i	−0.206956	+	0.978350i	$0.566356\pi$
$678$		0			0
$679$	64.7696			2.48563
$680$		0			0
$681$	−17.6569			−0.676612
$682$		0			0
$683$	−14.3431	−	14.3431i	−0.548825	−	0.548825i	0.377276	−	0.926101i	$-0.376861\pi$
$683$	−14.3431	−	14.3431i	−0.548825	−	0.548825i	−0.926101	+	0.377276i	$0.876861\pi$
$684$		0			0
$685$	−7.31371	−	7.31371i	−0.279442	−	0.279442i
$686$		0			0
$687$	−9.89949	+	9.89949i	−0.377689	+	0.377689i
$688$		0			0
$689$			8.00000i			0.304776i
$690$		0			0
$691$	9.17157	−	9.17157i	0.348903	−	0.348903i	−0.510798	−	0.859701i	$-0.670650\pi$
$691$	9.17157	−	9.17157i	0.348903	−	0.348903i	0.859701	+	0.510798i	$0.170650\pi$
$692$		0			0
$693$	−19.3137			−0.733667
$694$		0			0
$695$		−	3.71573i		−	0.140946i
$696$		0			0
$697$	12.6569	−	0.372583i	0.479413	−	0.0141126i
$698$		0			0
$699$		−	12.7279i		−	0.481414i
$700$		0			0
$701$	−23.5147			−0.888139			−0.444069	−	0.895992i	$-0.646466\pi$
$701$	−23.5147			−0.888139			−0.444069	+	0.895992i	$0.646466\pi$
$702$		0			0
$703$	−10.8284	+	10.8284i	−0.408402	+	0.408402i
$704$		0			0
$705$			7.31371i			0.275450i
$706$		0			0
$707$	−17.6569	+	17.6569i	−0.664054	+	0.664054i
$708$		0			0
$709$	−23.5858	−	23.5858i	−0.885783	−	0.885783i	0.108332	−	0.994115i	$-0.465449\pi$
$709$	−23.5858	−	23.5858i	−0.885783	−	0.885783i	−0.994115	+	0.108332i	$0.965449\pi$
$710$		0			0
$711$	10.2426	+	10.2426i	0.384129	+	0.384129i
$712$		0			0
$713$	−2.62742			−0.0983975
$714$		0			0
$715$	−6.62742			−0.247851
$716$		0			0
$717$	8.82843	+	8.82843i	0.329704	+	0.329704i
$718$		0			0
$719$	−7.21320	−	7.21320i	−0.269007	−	0.269007i	0.559693	−	0.828700i	$-0.310919\pi$
$719$	−7.21320	−	7.21320i	−0.269007	−	0.269007i	−0.828700	+	0.559693i	$0.810919\pi$
$720$		0			0
$721$	50.6274	−	50.6274i	1.88546	−	1.88546i
$722$		0			0
$723$			8.24264i			0.306547i
$724$		0			0
$725$	−1.92893	+	1.92893i	−0.0716387	+	0.0716387i
$726$		0			0
$727$	10.3431			0.383606			0.191803	−	0.981433i	$-0.438567\pi$
$727$	10.3431			0.383606			0.191803	+	0.981433i	$0.438567\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−4.68629	+	4.97056i	−0.173329	+	0.183843i
$732$		0			0
$733$		−	41.4558i		−	1.53121i	−0.643313	−	0.765603i	$-0.722441\pi$
$733$		−	41.4558i		−	1.53121i	0.643313	−	0.765603i	$-0.277559\pi$
$734$		0			0
$735$	−9.55635			−0.352491
$736$		0			0
$737$	−3.31371	+	3.31371i	−0.122062	+	0.122062i
$738$		0			0
$739$			9.17157i			0.337382i	0.985669	+	0.168691i	$0.0539540\pi$
$739$			9.17157i			0.337382i	−0.985669	+	0.168691i	$0.946046\pi$
$740$		0			0
$741$	13.6569	−	13.6569i	0.501697	−	0.501697i
$742$		0			0
$743$	22.2426	+	22.2426i	0.816003	+	0.816003i	0.985526	−	0.169523i	$-0.0542227\pi$
$743$	22.2426	+	22.2426i	0.816003	+	0.816003i	−0.169523	+	0.985526i	$0.554223\pi$
$744$		0			0
$745$	4.14214	+	4.14214i	0.151756	+	0.151756i
$746$		0			0
$747$	−4.48528			−0.164108
$748$		0			0
$749$	65.9411			2.40944
$750$		0			0
$751$	−8.10051	−	8.10051i	−0.295592	−	0.295592i	0.543693	−	0.839284i	$-0.317026\pi$
$751$	−8.10051	−	8.10051i	−0.295592	−	0.295592i	−0.839284	+	0.543693i	$0.817026\pi$
$752$		0			0
$753$	12.4853	+	12.4853i	0.454989	+	0.454989i
$754$		0			0
$755$	−5.65685	+	5.65685i	−0.205874	+	0.205874i
$756$		0			0
$757$		−	6.00000i		−	0.218074i	−0.994038	−	0.109037i	$-0.965223\pi$
$757$		−	6.00000i		−	0.218074i	0.994038	−	0.109037i	$-0.0347767\pi$
$758$		0			0
$759$	−8.97056	+	8.97056i	−0.325611	+	0.325611i
$760$		0			0
$761$	1.65685			0.0600609			0.0300305	−	0.999549i	$-0.490440\pi$
$761$	1.65685			0.0600609			0.0300305	+	0.999549i	$0.490440\pi$
$762$		0			0
$763$		−	18.8284i		−	0.681635i
$764$		0			0
$765$	2.41421	−	0.0710678i	0.0872861	−	0.00256946i
$766$		0			0
$767$		−	35.3137i		−	1.27510i
$768$		0			0
$769$	40.9706			1.47744			0.738718	−	0.674014i	$-0.235431\pi$
$769$	40.9706			1.47744			0.738718	+	0.674014i	$0.235431\pi$
$770$		0			0
$771$	20.7279	−	20.7279i	0.746498	−	0.746498i
$772$		0			0
$773$		−	44.6274i		−	1.60514i	−0.596560	−	0.802568i	$-0.703466\pi$
$773$		−	44.6274i		−	1.60514i	0.596560	−	0.802568i	$-0.296534\pi$
$774$		0			0
$775$	−2.72792	+	2.72792i	−0.0979899	+	0.0979899i
$776$		0			0
$777$	−7.65685	−	7.65685i	−0.274688	−	0.274688i
$778$		0			0
$779$	14.8284	+	14.8284i	0.531284	+	0.531284i
$780$		0			0
$781$	−25.9411			−0.928246
$782$		0			0
$783$	−0.585786			−0.0209343
$784$		0			0
$785$	2.48528	+	2.48528i	0.0887035	+	0.0887035i
$786$		0			0
$787$	15.5147	+	15.5147i	0.553040	+	0.553040i	0.927317	−	0.374277i	$-0.122109\pi$
$787$	15.5147	+	15.5147i	0.553040	+	0.553040i	−0.374277	+	0.927317i	$0.622109\pi$
$788$		0			0
$789$	−7.17157	+	7.17157i	−0.255315	+	0.255315i
$790$		0			0
$791$			61.4558i			2.18512i
$792$		0			0
$793$	−2.14214	+	2.14214i	−0.0760695	+	0.0760695i
$794$		0			0
$795$	−1.65685			−0.0587626
$796$		0			0
$797$		−	21.1716i		−	0.749936i	−0.927038	−	0.374968i	$-0.877654\pi$
$797$		−	21.1716i		−	0.749936i	0.927038	−	0.374968i	$-0.122346\pi$
$798$		0			0
$799$	37.4558	+	35.3137i	1.32509	+	1.24931i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	37.6569			1.32888
$804$		0			0
$805$	−6.34315	+	6.34315i	−0.223567	+	0.223567i
$806$		0			0
$807$			5.07107i			0.178510i
$808$		0			0
$809$	−31.4853	+	31.4853i	−1.10696	+	1.10696i	−0.113416	+	0.993548i	$0.536179\pi$
$809$	−31.4853	+	31.4853i	−1.10696	+	1.10696i	−0.993548	+	0.113416i	$0.963821\pi$
$810$		0			0
$811$	−20.4853	−	20.4853i	−0.719336	−	0.719336i	0.249134	−	0.968469i	$-0.419854\pi$
$811$	−20.4853	−	20.4853i	−0.719336	−	0.719336i	−0.968469	+	0.249134i	$0.919854\pi$
$812$		0			0
$813$	15.3137	+	15.3137i	0.537075	+	0.537075i
$814$		0			0
$815$	−1.37258			−0.0480795
$816$		0			0
$817$	−11.3137			−0.395817
$818$		0			0
$819$	9.65685	+	9.65685i	0.337438	+	0.337438i
$820$		0			0
$821$	9.72792	+	9.72792i	0.339507	+	0.339507i	0.856182	−	0.516675i	$-0.172830\pi$
$821$	9.72792	+	9.72792i	0.339507	+	0.339507i	−0.516675	+	0.856182i	$0.672830\pi$
$822$		0			0
$823$	−22.0416	+	22.0416i	−0.768323	+	0.768323i	−0.977811	−	0.209488i	$-0.932820\pi$
$823$	−22.0416	+	22.0416i	−0.768323	+	0.768323i	0.209488	+	0.977811i	$0.432820\pi$
$824$		0			0
$825$			18.6274i			0.648523i
$826$		0			0
$827$	26.8284	−	26.8284i	0.932916	−	0.932916i	−0.0649713	−	0.997887i	$-0.520696\pi$
$827$	26.8284	−	26.8284i	0.932916	−	0.932916i	0.997887	+	0.0649713i	$0.0206956\pi$
$828$		0			0
$829$	−27.9411			−0.970435			−0.485218	−	0.874393i	$-0.661260\pi$
$829$	−27.9411			−0.970435			−0.485218	+	0.874393i	$0.661260\pi$
$830$		0			0
$831$			9.75736i			0.338479i
$832$		0			0
$833$	−46.1421	+	48.9411i	−1.59873	+	1.69571i
$834$		0			0
$835$			12.7696i			0.441909i
$836$		0			0
$837$	−0.828427			−0.0286346
$838$		0			0
$839$	−1.75736	+	1.75736i	−0.0606708	+	0.0606708i	−0.736791	−	0.676120i	$-0.763660\pi$
$839$	−1.75736	+	1.75736i	−0.0606708	+	0.0606708i	0.676120	+	0.736791i	$0.263660\pi$
$840$		0			0
$841$		−	28.6569i		−	0.988167i
$842$		0			0
$843$	−13.6569	+	13.6569i	−0.470367	+	0.470367i
$844$		0			0
$845$	−2.07107	−	2.07107i	−0.0712469	−	0.0712469i
$846$		0			0
$847$	17.0711	+	17.0711i	0.586569	+	0.586569i
$848$		0			0
$849$	8.00000			0.274559
$850$		0			0
$851$	−7.11270			−0.243820
$852$		0			0
$853$	34.2132	+	34.2132i	1.17144	+	1.17144i	0.981867	+	0.189571i	$0.0607096\pi$
$853$	34.2132	+	34.2132i	1.17144	+	1.17144i	0.189571	+	0.981867i	$0.439290\pi$
$854$		0			0
$855$	2.82843	+	2.82843i	0.0967302	+	0.0967302i
$856$		0			0
$857$	−11.1421	+	11.1421i	−0.380608	+	0.380608i	−0.871321	−	0.490713i	$-0.836736\pi$
$857$	−11.1421	+	11.1421i	−0.380608	+	0.380608i	0.490713	+	0.871321i	$0.336736\pi$
$858$		0			0
$859$			1.65685i			0.0565311i	0.999600	+	0.0282656i	$0.00899841\pi$
$859$			1.65685i			0.0565311i	−0.999600	+	0.0282656i	$0.991002\pi$
$860$		0			0
$861$	−10.4853	+	10.4853i	−0.357337	+	0.357337i
$862$		0			0
$863$	−5.65685			−0.192562			−0.0962808	−	0.995354i	$-0.530695\pi$
$863$	−5.65685			−0.192562			−0.0962808	+	0.995354i	$0.530695\pi$
$864$		0			0
$865$			2.40202i			0.0816711i
$866$		0			0
$867$	11.2929	−	12.7071i	0.383527	−	0.431556i
$868$		0			0
$869$		−	57.9411i		−	1.96552i
$870$		0			0
$871$	3.31371			0.112281
$872$		0			0
$873$	9.48528	−	9.48528i	0.321028	−	0.321028i
$874$		0			0
$875$			27.3137i			0.923372i
$876$		0			0
$877$	8.55635	−	8.55635i	0.288927	−	0.288927i	−0.547729	−	0.836656i	$-0.684507\pi$
$877$	8.55635	−	8.55635i	0.288927	−	0.288927i	0.836656	+	0.547729i	$0.184507\pi$
$878$		0			0
$879$	−6.58579	−	6.58579i	−0.222133	−	0.222133i
$880$		0			0
$881$	20.6569	+	20.6569i	0.695947	+	0.695947i	0.963534	−	0.267587i	$-0.0862262\pi$
$881$	20.6569	+	20.6569i	0.695947	+	0.695947i	−0.267587	+	0.963534i	$0.586226\pi$
$882$		0			0
$883$	48.7696			1.64123			0.820613	−	0.571484i	$-0.193632\pi$
$883$	48.7696			1.64123			0.820613	+	0.571484i	$0.193632\pi$
$884$		0			0
$885$	7.31371			0.245848
$886$		0			0
$887$	1.27208	+	1.27208i	0.0427122	+	0.0427122i	0.728140	−	0.685428i	$-0.240385\pi$
$887$	1.27208	+	1.27208i	0.0427122	+	0.0427122i	−0.685428	+	0.728140i	$0.740385\pi$
$888$		0			0
$889$	46.6274	+	46.6274i	1.56383	+	1.56383i
$890$		0			0
$891$	−2.82843	+	2.82843i	−0.0947559	+	0.0947559i
$892$		0			0
$893$			85.2548i			2.85294i
$894$		0			0
$895$	−5.37258	+	5.37258i	−0.179586	+	0.179586i
$896$		0			0
$897$	8.97056			0.299518
$898$		0			0
$899$			0.485281i			0.0161850i
$900$		0			0
$901$	−8.00000	+	8.48528i	−0.266519	+	0.282686i
$902$		0			0
$903$		−	8.00000i		−	0.266223i
$904$		0			0
$905$	−4.62742			−0.153821
$906$		0			0
$907$	8.97056	−	8.97056i	0.297863	−	0.297863i	−0.542314	−	0.840176i	$-0.682452\pi$
$907$	8.97056	−	8.97056i	0.297863	−	0.297863i	0.840176	+	0.542314i	$0.182452\pi$
$908$		0			0
$909$			5.17157i			0.171530i
$910$		0			0
$911$	−20.5858	+	20.5858i	−0.682038	+	0.682038i	−0.960459	−	0.278421i	$-0.910189\pi$
$911$	−20.5858	+	20.5858i	−0.682038	+	0.682038i	0.278421	+	0.960459i	$0.410189\pi$
$912$		0			0
$913$	12.6863	+	12.6863i	0.419855	+	0.419855i
$914$		0			0
$915$	−0.443651	−	0.443651i	−0.0146666	−	0.0146666i
$916$		0			0
$917$	−93.2548			−3.07955
$918$		0			0
$919$	18.3431			0.605085			0.302542	−	0.953136i	$-0.402165\pi$
$919$	18.3431			0.605085			0.302542	+	0.953136i	$0.402165\pi$
$920$		0			0
$921$	−4.48528	−	4.48528i	−0.147795	−	0.147795i
$922$		0			0
$923$	12.9706	+	12.9706i	0.426931	+	0.426931i
$924$		0			0
$925$	−7.38478	+	7.38478i	−0.242810	+	0.242810i
$926$		0			0
$927$		−	14.8284i		−	0.487029i
$928$		0			0
$929$	30.1127	−	30.1127i	0.987966	−	0.987966i	−0.0119629	−	0.999928i	$-0.503808\pi$
$929$	30.1127	−	30.1127i	0.987966	−	0.987966i	0.999928	+	0.0119629i	$0.00380799\pi$
$930$		0			0
$931$	−111.397			−3.65089
$932$		0			0
$933$			0.828427i			0.0271215i
$934$		0			0
$935$	−7.02944	−	6.62742i	−0.229887	−	0.216740i
$936$		0			0
$937$			4.00000i			0.130674i	0.997863	+	0.0653372i	$0.0208123\pi$
$937$			4.00000i			0.130674i	−0.997863	+	0.0653372i	$0.979188\pi$
$938$		0			0
$939$	−10.1005			−0.329618
$940$		0			0
$941$	−24.2132	+	24.2132i	−0.789328	+	0.789328i	−0.981384	−	0.192056i	$-0.938484\pi$
$941$	−24.2132	+	24.2132i	−0.789328	+	0.789328i	0.192056	+	0.981384i	$0.438484\pi$
$942$		0			0
$943$			9.74012i			0.317182i
$944$		0			0
$945$	−2.00000	+	2.00000i	−0.0650600	+	0.0650600i
$946$		0			0
$947$	15.5147	+	15.5147i	0.504161	+	0.504161i	0.912728	−	0.408567i	$-0.133972\pi$
$947$	15.5147	+	15.5147i	0.504161	+	0.504161i	−0.408567	+	0.912728i	$0.633972\pi$
$948$		0			0
$949$	−18.8284	−	18.8284i	−0.611197	−	0.611197i
$950$		0			0
$951$	21.5563			0.699013
$952$		0			0
$953$	7.02944			0.227706			0.113853	−	0.993498i	$-0.463681\pi$
$953$	7.02944			0.227706			0.113853	+	0.993498i	$0.463681\pi$
$954$		0			0
$955$	−0.485281	−	0.485281i	−0.0157033	−	0.0157033i
$956$		0			0
$957$	1.65685	+	1.65685i	0.0535585	+	0.0535585i
$958$		0			0
$959$	60.2843	−	60.2843i	1.94668	−	1.94668i
$960$		0			0
$961$		−	30.3137i		−	0.977862i
$962$		0			0
$963$	9.65685	−	9.65685i	0.311188	−	0.311188i
$964$		0			0
$965$	−3.45584			−0.111248
$966$		0			0
$967$		−	18.1421i		−	0.583412i	−0.956508	−	0.291706i	$-0.905777\pi$
$967$		−	18.1421i		−	0.583412i	0.956508	−	0.291706i	$-0.0942228\pi$
$968$		0			0
$969$	28.1421	−	0.828427i	0.904056	−	0.0266129i
$970$		0			0
$971$		−	20.4853i		−	0.657404i	−0.944434	−	0.328702i	$-0.893389\pi$
$971$		−	20.4853i		−	0.657404i	0.944434	−	0.328702i	$-0.106611\pi$
$972$		0			0
$973$	30.6274			0.981870
$974$		0			0
$975$	9.31371	−	9.31371i	0.298277	−	0.298277i
$976$		0			0
$977$		−	0.284271i		−	0.00909464i	−0.999990	−	0.00454732i	$-0.998553\pi$
$977$		−	0.284271i		−	0.00909464i	0.999990	−	0.00454732i	$-0.00144746\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−2.75736	−	2.75736i	−0.0880357	−	0.0880357i
$982$		0			0
$983$	−3.41421	−	3.41421i	−0.108897	−	0.108897i	0.650559	−	0.759456i	$-0.274535\pi$
$983$	−3.41421	−	3.41421i	−0.108897	−	0.108897i	−0.759456	+	0.650559i	$0.774535\pi$
$984$		0			0
$985$	−6.00000			−0.191176
$986$		0			0
$987$	−60.2843			−1.91887
$988$		0			0
$989$	−3.71573	−	3.71573i	−0.118153	−	0.118153i
$990$		0			0
$991$	−38.5269	−	38.5269i	−1.22385	−	1.22385i	−0.966253	−	0.257595i	$-0.917070\pi$
$991$	−38.5269	−	38.5269i	−1.22385	−	1.22385i	−0.257595	−	0.966253i	$-0.582930\pi$
$992$		0			0
$993$	−13.1716	+	13.1716i	−0.417987	+	0.417987i
$994$		0			0
$995$			0.485281i			0.0153845i
$996$		0			0
$997$	32.8995	−	32.8995i	1.04194	−	1.04194i	0.0428562	−	0.999081i	$-0.486354\pi$
$997$	32.8995	−	32.8995i	1.04194	−	1.04194i	0.999081	−	0.0428562i	$-0.0136457\pi$
$998$		0			0
$999$	−2.24264			−0.0709540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	816.2.bd.a.625.1		4
3.2	odd	2		2448.2.be.t.1441.1		4
4.3	odd	2		102.2.f.a.13.2	✓	4
12.11	even	2		306.2.g.g.217.1		4
17.4	even	4	inner	816.2.bd.a.769.1		4
51.38	odd	4		2448.2.be.t.1585.1		4
68.15	odd	8		1734.2.a.n.1.1		2
68.19	odd	8		1734.2.a.o.1.2		2
68.43	odd	8		1734.2.b.h.577.4		4
68.47	odd	4		1734.2.f.i.1483.1		4
68.55	odd	4		102.2.f.a.55.2	yes	4
68.59	odd	8		1734.2.b.h.577.1		4
68.67	odd	2		1734.2.f.i.829.1		4
204.83	even	8		5202.2.a.o.1.2		2
204.155	even	8		5202.2.a.x.1.1		2
204.191	even	4		306.2.g.g.55.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.2.f.a.13.2	✓	4	4.3	odd	2
102.2.f.a.55.2	yes	4	68.55	odd	4
306.2.g.g.55.1		4	204.191	even	4
306.2.g.g.217.1		4	12.11	even	2
816.2.bd.a.625.1		4	1.1	even	1	trivial
816.2.bd.a.769.1		4	17.4	even	4	inner
1734.2.a.n.1.1		2	68.15	odd	8
1734.2.a.o.1.2		2	68.19	odd	8
1734.2.b.h.577.1		4	68.59	odd	8
1734.2.b.h.577.4		4	68.43	odd	8
1734.2.f.i.829.1		4	68.67	odd	2
1734.2.f.i.1483.1		4	68.47	odd	4
2448.2.be.t.1441.1		4	3.2	odd	2
2448.2.be.t.1585.1		4	51.38	odd	4
5202.2.a.o.1.2		2	204.83	even	8
5202.2.a.x.1.1		2	204.155	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.bd (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(0.414214 + 0.414214i) q^{5} +(-3.41421 + 3.41421i) q^{7} +1.00000i q^{9} +(2.82843 - 2.82843i) q^{11} -2.82843 q^{13} -0.585786i q^{15} +(-3.00000 - 2.82843i) q^{17} -6.82843i q^{19} +4.82843 q^{21} +(2.24264 - 2.24264i) q^{23} -4.65685i q^{25} +(0.707107 - 0.707107i) q^{27} +(-0.414214 - 0.414214i) q^{29} +(-0.585786 - 0.585786i) q^{31} -4.00000 q^{33} -2.82843 q^{35} +(-1.58579 - 1.58579i) q^{37} +(2.00000 + 2.00000i) q^{39} +(-2.17157 + 2.17157i) q^{41} -1.65685i q^{43} +(-0.414214 + 0.414214i) q^{45} -12.4853 q^{47} -16.3137i q^{49} +(0.121320 + 4.12132i) q^{51} -2.82843i q^{53} +2.34315 q^{55} +(-4.82843 + 4.82843i) q^{57} +12.4853i q^{59} +(0.757359 - 0.757359i) q^{61} +(-3.41421 - 3.41421i) q^{63} +(-1.17157 - 1.17157i) q^{65} -1.17157 q^{67} -3.17157 q^{69} +(-4.58579 - 4.58579i) q^{71} +(6.65685 + 6.65685i) q^{73} +(-3.29289 + 3.29289i) q^{75} +19.3137i q^{77} +(10.2426 - 10.2426i) q^{79} -1.00000 q^{81} +4.48528i q^{83} +(-0.0710678 - 2.41421i) q^{85} +0.585786i q^{87} +(9.65685 - 9.65685i) q^{91} +0.828427i q^{93} +(2.82843 - 2.82843i) q^{95} +(-9.48528 - 9.48528i) q^{97} +(2.82843 + 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} - 8 q^{7} - 12 q^{17} + 8 q^{21} - 8 q^{23} + 4 q^{29} - 8 q^{31} - 16 q^{33} - 12 q^{37} + 8 q^{39} - 20 q^{41} + 4 q^{45} - 16 q^{47} - 8 q^{51} + 32 q^{55} - 8 q^{57} + 20 q^{61} - 8 q^{63}+ \cdots - 4 q^{97}+O(q^{100}) \) 4 * q - 4 * q^5 - 8 * q^7 - 12 * q^17 + 8 * q^21 - 8 * q^23 + 4 * q^29 - 8 * q^31 - 16 * q^33 - 12 * q^37 + 8 * q^39 - 20 * q^41 + 4 * q^45 - 16 * q^47 - 8 * q^51 + 32 * q^55 - 8 * q^57 + 20 * q^61 - 8 * q^63 - 16 * q^65 - 16 * q^67 - 24 * q^69 - 24 * q^71 + 4 * q^73 - 16 * q^75 + 24 * q^79 - 4 * q^81 + 28 * q^85 + 16 * q^91 - 4 * q^97

Introduction

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